A set of narrow vertical slits is located a distance D from a screen. The slits

Question

A set of narrow vertical slits is located a distance D from a screen. The slits are equally spaced and have the same width. The intensity pattern in the figure is observed when light from a laser passes through the slits, illuminating them uniformly. The screen is perpendicular to the direction of the light. What is the spacing between the slits?
Data: Distance to the screen = 2.23 meters;
Wavelength of light = 570 nanometers;
Distance between tick marks on the intensity figure = 1.60 centimeters

Explanation / Answer

Distance to the screen = 2.77 meters; Wavelength of light = 0.420 micrometers; Distance between tick marks on the intensity figure = 1.60 cm (The figure has the generic diffraction grating light pattern, with tick marks occurring between each maxima)

Maxima occur at sin theta = m lambda / d (where m is the order, lambda is the wavelength of light, and d is the distance between slits)

first.. I find out what theta is.. i can find this by
tan theta = (.016m)/(2.77m)
tan theta = .0057761
theta = .33095 degrees

plugging into the maxima formula,
sin theta = m lambda / d
sin (.33095) = 1 (.420x10^-6) / d
d = 7.27x10^-5m = 72.7 micrometers

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